Phenomenology of a pseudoscalar glueball

and charmed mesons in a chiral symmetric

Model Walaa I. Eshraim

Prof. Dr. Dirk H. Rischke

Thanks to

Workshop on Strangeness and Hadron Physics at J-PARC, KEK Tokai campus, Japan, August 7th , 2015

W. I. Eshraim

• Quantum Chromodynamics: QCD

- Symmetries of the QCD Lagrangian.

if all quark massless then we have chiral symmetry

- Spontaneous breaking of chiral symmetry by quark condensates

- Explicit breaking of global chiral symmetry by quark masses and chiral anomaly

• Effective chiral models of QCD.

• Development of a chirally symmetric model for mesons.

„Extended Linear Sigma Model (eLSM)‟

Introduction

AVlfrflfrf UUNSUNSUNUNU )1()1()()()()(

W. I. Eshraim

• Decay of the pseudoscalar glueball into scalar and pseudoscalar

mesons.

• Linear sigma model with vector and axial vector degrees of

freedom.

• Inclusion of the charmed mesons into the linear sigma model

(extended Linear Sigma Model - eLSM).

• Extension from low-energy to high-energy mesons.

• Study of the model for T = μ =0 (spectroscopy in vacuum).

Motivation

,

W. I. Eshraim

Fields of the model DAAD

• Mesons: quark-antiquark states ( )

(scalar, pseudoscalar, vector and axialvector quarkonia.)

Quantum number: • Glueballs (additional mesons): The scalar and the pseudoscalar glueball. • Baryons: nucleon doublet and its partner (in the so-called mirror assignment)

P CJ nConjugatio Charge

Parity

Spin Total

W. I. Eshraim

Construction of the eLSM

The construction of the so-called Extended Linear Sigma Model based on • dilatation invariance Note that: The breaking of the dilatation symmetry is only included in the “gluonic part” (scalar glueball and axial anomaly) • chiral invariance Furthermore, the invariance under C and P is also taken into account.

Vlfrf UNSUNSU )1()()(

W. I. Eshraim

The eLSM Lagrangian with (axial-)vector mesons

D.Parganlija, P.Kovacs, G.Wolf, F.Giacosa and D.H. Rischke,

Phys. Rev. D 87 (2013) 014011 [arXiv:1208.0585 [hep-ph]];

W. I. Eshraim, PoS QCD -TNT-III (2014) 049

[arXiv:1401.3260 [hep-ph]].

+chirally invariant vector and axialvector four-point interaction vertices

44

Decays of the pseudoscalar glueball

With scalar and pseudoscalar mesons

• There fulfill chiral symmetry but breaks the axial anomaly.

• Only one unknown constant. All the rest is fied.

The branching ratio of decays are predicted

With nucleons in the framework of the so-called mirror assignment

Interaction Lagrangian for the pseudoscalar glueball:

W. I. Eshraim

W. I. Eshraim

Mass of a pseudoscalar glueball

Lattice QCD calculation

[C. Morningstar and M. J. Peardon, AIP Conf. Proc. 688, 220 (2004)

[arXiv:nucl-th/0309068]];

The Pseudoscalar Glueball at the

border within light and heavy

0

0

6.2~

I

J

M

PC

G

Ğ gg

GeV

- Predict branching ratios for decays into three pseudoscalar mesons

W. I. Eshraim; S. Janowski; F. Giacosa; D. H.

Rischke. Phys.Rev. D87 (2013) 054036 [arXiv:

1208.6474 [hep-ph].

PANDA/FAIR will be able to

scan the energy above 2.5 GeV

BESIII has measured a

candidate: X(2370)

The decay of the pseudoscalar glueball into three pions vanishes:

W. I. Eshraim

Predict branching ratios for decays into a scalar and a pseudoscalar meson

W. I. Eshraim; S. Janowski; F. Giacosa; D. H. Rischke. Phys.Rev. D87 (2013) 054036 [arXiv: 1208.6474 [hep-ph]; W.I. Eshraim and S. Janowski,

PoS ConfinementX 118, (2012) [arXiv:1301.3345 [hep-ph]]; W.I. Eshraim and S. Janowski, J. Phys.Conf. Ser. 426, 012018 (2013) [arXiv:1211.7323

[hep-ph]].

Could be measured by PANDA!

whereas

The full width of the pseudoscalar glueball is expected to be small

)1710(),1370(),1450(),1430( 0000

*

0 ffaaKK SNs

W. I. Eshraim

The branching ratio of the decay processes and

Remark: The pseudoscalar glueball can be produced directly through a

fusion process in proton-proton collision

Charmed mesons

in the extended Linear Sigma Model

2e

W. I. Eshraim

• Linear sigma model with vector and axial vector degrees of

freedom.

• Inclusion of the charmed mesons into the linear sigma model

(extended Linear Sigma Model - eLSM).

• Extension from low-energy to high-energy mesons.

• Study of the model for T = μ =0 (spectroscopy in vacuum).

DAAD Fields in the model • Mesons: quark-antiquark states ( )

• For Nf = 4 there are 66 mesons: 64 quark-antiquark fields + one pseudoscalar glueball

+one scalar glueball G

Scalar mesons: Pseudoscalar mesons: Vector mesons: Axial-vector mesons:

W. I. Eshraim

qq

pcJQuantum numbers ( )

G~

PCJ

10 10

fields 24N2

f

0*

0

0*

0 )2400(DD

)2317(*

0

*

0 SS DD

)2400(*

0

*

0 DD

)1(00 Pcc

0DD

sD

)1( SCC

0*0* )2007(DD

)2010(** DD

SD

)1(// SJJ

0

1

0

1 )2420(DD )2420(11 DD )2536(11 SS DD

)1(00 Pcc

W. I. Eshraim, PoS QCD -TNT-III (2014) 049 [arXiv:1401.3260 [hep-ph]]; W. I. Eshraim, F. Giacosa, and D. H. Rischke , [arXiv:1405.5861 [hep-ph]].

W. I. Eshraim

Including charm degree of freedom

1) Pseudoscalar fields: 2) Scalar fields:

and

with mixing angle

The multiplet of the scalar and pseudoscalar quark-antiquark states:

3) Vector fields: 4) Axial vector fields:

The left-handed matrix: and the right-handed matrix:

W. I. Eshraim, PoS QCD -TNT-III (2014) 049 [arXiv:1401.3260 [hep-ph]]; W. I. Eshraim; Giacosa; and D. H. Rischke; [arXiv:1405.5861 [hep-ph]]

iPS

AVL AVR

[ W. I. Eshraim; S. Janowski; F. Giacosa; D.

H. Rischke. Phys.Rev. D87 (2013) 054036

[arXiv: 1208.6474 [hep-ph]].

o6.44

W. I. Eshraim

Spontaneous Symmetry Breaking (SSB)

Shifting the fields

, ,

where

,

For Nf = 4 new shift

where

There are 29 eqs. for the squared masses of mesons with 15 unknown parameters.

W. I. Eshraim, PoS QCD -TNT-III (2014) 049 [arXiv:1401.3260 [hep-ph]];

D. Parganlija, P. Kovacs, G. Wolf, F. Giacosa and D. H. Rischke, Phys. Rev. D 87 (2013) 014011 [arXiv:1208.0585 [hep-ph].

W. I. Eshraim, F. Giacosa and D. H. Rischke, , arXiv:1405.5861 [hep-ph]].

W. I. Eshraim

Parameters

The values of the Nf = 3 parameters :

[D. Parganlija, P. Kovacs, G.

Wolf, F. Giacosa and D. H.

Rischke, Phys. Rev. D 87

(2013) 014011

[arXiv:1208.0585 [hep-ph]].

The new three parameters for Nf = 4 are .

By fit with /d.o.f = 1 :

[ W. I. Eshraim, F. Giacosa and D. H. Rischke, , arXiv:1405.5861 [hep-ph]].

CCC ,,

/d.o.f = 1.23

W. I. Eshraim

Results

Masses of light mesons:

W. I. Eshraim, PoS QCD -TNT-III (2014) 049 [arXiv:1401.3260 [hep-ph]; D. Parganlija, P. Kovacs, G. Wolf, F. Giacosa and D.

H. Rischke, Phys. Rev. D 87 (2013) 014011 [arXiv:1208.0585 [hep-ph].

W. I. Eshraim

Masses of (open and hidden) charmed mesons:

W. I. Eshraim, F. Giacosa and D. H. Rischke, [arXiv:1405.5861 [hep-ph]];

W. I. Eshraim, PoS QCD -TNT-III (2014) 049 [arXiv:1401.3260 [hep-ph].

W. I. Eshraim

The mass difference of the squared charmed (axial-)vector mesons:

Weak decay constant of D, DS, and .

[Exp. value = 206.7 ± 8.9 ] [Exp. value = 260.5 ± 5.4] [Exp. value = 335 ± 75]

W. I. Eshraim, F. Giacosa and D. H. Rischke, arXiv:1405.5861 [hep-ph].

Mass difference and decay constants

MeV MeV, MeV,

W. I. Eshraim

Decay widths of open charmed mesons:

W. I. Eshraim, F. Giacosa and D. H. Rischke, arXiv:1405.5861 [hep-ph].

W. I. Eshraim

Mixing matrix of the three scalar fields (σN, σs, G)

where G is a scalar glueball. S. Janowski, F. Giacosa and D. H. Rischke, Phys.Rev. D90 (2014) 114005 [ arXiv:1408.4921 [hep-ph]].

• The decay widths of charmonium state depend on the parameters λ1 and h1.

Using fit including the decay widths of charmonium state , we obtain

λ1= -0.16 and h1= 0.046.

W. I. Eshraim and D. H. Rischke, in preparation, preliminary!

0C

Decay widths of hidden charmed mesons:

W. I. Eshraim

2) Decay widths of scalar charmonium state ( ): C

W. I. Eshraim and D. H. Rischke, in

preparation preliminary!

Decay widths of hidden charmed mesons:

1) Decay widths of (axial-)vector charmonium states:

0/ J0

1

cand

W. I. Eshraim and D. H. Rischke, in preparation

Decay width of into a pseudoscalar glueball C

GC~

16.0

BESIII:

MeV

MeV 124.0

2600~ G

m

2370~ G

m MeV

MeV

W. I. Eshraim

Lattice QCD calculations:

Could be measured by

Decay width of c0

3) Decay widths of a pseudoscalar charmonium state ( ): c0

W. I. Eshraim and D. H. Rischke, in preparation, preliminary!

W. I. Eshraim

W. I. Eshraim

Conclusions and Outlook

1. In the case of : Decay of a pseudoscalar glueball with a mass above 2 GeV.

2. Linear sigma model with Nf = 4 and vector and axial-vector mesons.

3. Masses of (open and hidden) charmed mesons.

4. Charm-anticharm condensate and decay constants.

5. Decay widths of (open and hidden) charmed mesons.

3fN